In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multipli...In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multiplicative derivations and show that every Boolean algebra is isomorphic to the algebra of all implicative derivations.Finally,we show that the sets of multiplicative and implicative derivations on bounded regular idempotent semihoops are in oneto-one correspondence.展开更多
In this paper, we investigate the Galois connections between two partially ordered objects in an arbitrary elementary topos. Some characterizations of Galois adjunctions which is similar to the classical case are obta...In this paper, we investigate the Galois connections between two partially ordered objects in an arbitrary elementary topos. Some characterizations of Galois adjunctions which is similar to the classical case are obtained by means of the diagram proof. This shows that the diagram method can be used to reconstruct the classical order theory in an arbitrary elementary topos.展开更多
形式概念分析理论已经广泛地应用于计算机诸多领域.当前,模糊概念格直接构造仍然是该领域主要问题之一,其构造过程具有指数级时间复杂度.为了提高模糊概念格构造效率,文中对串行模糊概念构造算法进行并行化改进,将模糊集合组合搜索空间...形式概念分析理论已经广泛地应用于计算机诸多领域.当前,模糊概念格直接构造仍然是该领域主要问题之一,其构造过程具有指数级时间复杂度.为了提高模糊概念格构造效率,文中对串行模糊概念构造算法进行并行化改进,将模糊集合组合搜索空间映射为自然数区间,简化了搜索空间表示、划分和遍历过程,进而提出并行模糊概念构造算法(Parallel Fuzzy Next Closure,ParaFuNeC).该算法对搜索空间均匀划分,子搜索空间彼此独立,从而避免并行任务之间同步、通讯等时间耗费,达到提高模糊概念构造效率的目标.时间复杂度分析和实验结果表明该算法在大规模计算任务情况下,加速比随着并行度的提高呈正比增长趋势.另外,串行比例指标表明ParaFuNeC算法在大规模计算任务情况下具有更好的可扩展性.展开更多
基金Supported by the National Natural Science Foundation of China(12271319).
文摘In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multiplicative derivations and show that every Boolean algebra is isomorphic to the algebra of all implicative derivations.Finally,we show that the sets of multiplicative and implicative derivations on bounded regular idempotent semihoops are in oneto-one correspondence.
基金Supported by the National Natural Science Foundation of China (Grant No.10731050)
文摘In this paper, we investigate the Galois connections between two partially ordered objects in an arbitrary elementary topos. Some characterizations of Galois adjunctions which is similar to the classical case are obtained by means of the diagram proof. This shows that the diagram method can be used to reconstruct the classical order theory in an arbitrary elementary topos.
文摘形式概念分析理论已经广泛地应用于计算机诸多领域.当前,模糊概念格直接构造仍然是该领域主要问题之一,其构造过程具有指数级时间复杂度.为了提高模糊概念格构造效率,文中对串行模糊概念构造算法进行并行化改进,将模糊集合组合搜索空间映射为自然数区间,简化了搜索空间表示、划分和遍历过程,进而提出并行模糊概念构造算法(Parallel Fuzzy Next Closure,ParaFuNeC).该算法对搜索空间均匀划分,子搜索空间彼此独立,从而避免并行任务之间同步、通讯等时间耗费,达到提高模糊概念构造效率的目标.时间复杂度分析和实验结果表明该算法在大规模计算任务情况下,加速比随着并行度的提高呈正比增长趋势.另外,串行比例指标表明ParaFuNeC算法在大规模计算任务情况下具有更好的可扩展性.
